﻿Solution of Equations, £97 



This does not constitute a very handy criterion, but it may 

 be greatly improved in the following way. 



In the first place, it is quite the same to the second linkage, 

 so far as its projection and motion are concerned, whether it 

 is actuated by the first by the proper connexion at the first 

 or at the final chords of the polygons, or indeed at any 

 parallel pair of chords, for each chord of the second or sine 

 polygon is parallel to a corresponding chord of the cosine 

 polygon, but the two have to be projected in directions at 

 right angles one to the other. 



If, therefore, the sine polygon can be bodily turned 

 through an angle o£ —90°, it will then have to be projected 

 in the same direction as the cosine polygon; and if the 

 mechanism of connexion retains the extremities of the 

 polygons together, and at the same time maintains the re- 

 quired proportionality among the chords generally, the 

 criterion will simply amount to finding the first point of 

 the sine polygon, now the final point of the whole train, in 

 the line Oy. 



The appropriate connexion is indicated in fig? 4. H n , r n 



Fig. 4. 



are the two chords, having their extremities together, and 

 maintained in that condition by a pin common to the two 

 kites, which have to be maintained at right angles. 



If the vertices of the smaller isosceles triangles are as in 

 Phil Mag. S. 6. Vol. 23. No. 138. June 1912. ' 3 N 



